predicate calculus

predicate calculus
The logical calculus in which the expressions include predicate letters, variables, and quantifiers, names, and operation letters, as well as the expressions for truth-functions and the propositional variables of the propositional calculus . The predicate calculus is the heart of modern logic, having proved capable of formalizing the central reasoning processes of modern mathematics and science. In a first-order predicate calculus the variables range over objects; in a higher-order calculus they may range over predicates and functions themselves. The first-order predicate calculus with identity includes ‘=’ as a primitive (undefined) expression: in a higher-order calculus it may be defined by the law that x = y iff (∀F)(Fx ↔ Fy ).

Philosophy dictionary. . 2011.

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  • predicate calculus — Logic. See functional calculus. Also called predicate logic. [1945 50] * * * Part of modern symbolic logic which systematically exhibits the logical relations between propositions involving quantifiers such as all and some. The predicate calculus …   Universalium

  • predicate calculus — noun Date: 1950 the branch of symbolic logic that uses symbols for quantifiers and for arguments and predicates of propositions as well as for unanalyzed propositions and logical connectives called also functional calculus compare propositional… …   New Collegiate Dictionary

  • predicate calculus — noun The branch of logic that deals with quantified statements such as there exists an x such that... or for any x, it is the case that... , where x is a member of the domain of discourse. See Also: predicate logic …   Wiktionary

  • predicate calculus — pred′icate cal′culus n. pho functional calculus • Etymology: 1945–50 …   From formal English to slang

  • predicate calculus — noun a system of symbolic logic that represents individuals and predicates and quantification over individuals (as well as the relations between propositions) • Syn: ↑functional calculus • Hypernyms: ↑symbolic logic, ↑mathematical logic, ↑formal… …   Useful english dictionary

  • predicate calculus — noun the branch of symbolic logic concerned with propositions containing predicates, names, and quantifiers …   English new terms dictionary

  • Monadic predicate calculus — In logic, the monadic predicate calculus is the fragment of predicate calculus in which all predicate letters are monadic (that is, they take only one argument), and there are no function letters. All atomic formulae have the form P(x), where P… …   Wikipedia

  • Calculus (disambiguation) — Calculus is Latin for pebble, and has a number of meanings in English: In mathematics and computer science Calculus , in its most general sense, is any method or system of calculation. To modern theoreticians the answer to the question what is a… …   Wikipedia

  • Predicate variable — In first order logic, a predicate variable is a predicate letter which can stand for a relation (between terms) but which has not been specifically assigned any particular relation (or meaning). In first order logic (FOL) they can be more… …   Wikipedia

  • Predicate logic — In mathematical logic, predicate logic is the generic term for symbolic formal systems like first order logic, second order logic, many sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulas… …   Wikipedia

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